The leaders of the 16 countries using Europe's single currency called an emergency summit today to try to avert a euro meltdown triggered by Greece's financial collapse.

Wrestling with the worst crisis in the common currency's 11 years and accused of fiddling for three months while Greece went up in flames, Angela Merkel of Germany, Nicolas Sarkozy of France and other European leaders are to meet in Brussels on May 10 to unlock tens of billions of euros for Athens to put out the fire.

The summit will be only the second time in the currency's history that the leaders have met as the "eurogroup". The first time was in Paris in October 2008 to concoct a response to the international banking and financial collapse. Gordon Brown also took part in the Paris summit, although Britain is not in the euro. This time, four days after May 6, a British prime minister will not be invited.

The crisis erupted last October when a new Greek government came into office to reveal that the previous regime had lied and cheated for years over the country's economic health, that Greece was living way beyond its means, that its deficit and national debt levels were unsustainable.

Six months later, Greece is in effect insolvent, on the brink of the common currency's first case of sovereign debt default unless it is bailed out.

That presents the other 15 governments of the eurozone, notably Germany, the EU's traditional paymaster, with its biggest challenge and its worst dilemma.

Greece threatens to expose the euro as a fair-weather currency, highlighting the multiple contradictions and inherent frailties of trying to marry the economic realities of 16 different countries. When the going gets tough, it shows the lack of proper fiscal and economic policy instruments to underpin a currency union.

"The time for horse-trading, prevarication and posturing is over. Arguably, the very future of the euro area is now teetering on a knife edge," said Colin Ellis, economist at Daiwa Capital Markets.

With the markets also testing the resilience of another two south European single-currency countries – Portugal and Spain – Angel Gurria, head of the Organisation for Economic Co-operation and Development, waxed apocalyptic, comparing the Greek collapse and its wider impact to the ebola virus.

For weeks the markets have been gambling mercilessly on a Greek default while pushing the costs of Greek borrowing to unaffordable levels. Europe's political leaders have appeared persistently behind the curve. They maintain they have acted swiftly and consistently all along. The evidence is less than persuasive.

Since February 11, they have sought to calm the markets and force down the rates on Greek borrowing, and hoped they would never have to implement their "last resort" bailout package.

That strategy has failed. In February, the yield on benchmark 10-year Greek bonds – the cost of short-term borrowing – was 5-6%. It is now 9-10%. While the billions will now have to be disbursed, the word from Berlin today was that more than €45bn is needed this year alone, with more to come over the following two years. A figure of €120bn was mentioned.

Balking as never before at being the EU's cashpoint, Germany has been the main obstacle, although others have also hidden behind Berlin and quietly egged it on. Merkel is the pivotal figure, but has been the main brake on concerted European action since governments embarked on their lacklustre exercise in crisis management.

Without Berlin, there is no bailout. Germany is obliged to shoulder the biggest bill, but the rescue is hugely contested and unpopular. Merkel appears to have little choice now but to bow to the inevitable.

"If we don't fix it in Greece, it may have a lot of consequences on the EU," warned Dominique Strauss-Kahn, head of the International Monetary Fund.

After weeks of stonewalling, Merkel pledged today to move quickly to shore up the common currency, while voicing her exasperation with Greek profligacy. She has used the crisis previously to demand a rewrite of the euro rulebook to expel countries misbehaving as badly as Greece. Today she added pointedly that Greece should probably never have been allowed to join in the first place.

Bild Zeitung, the normally supportive tabloid, is waging a ferocious campaign against the Greeks. With Germany needed to put up at least €8.4bn for Greece at a time of austerity and budget cuts at home, Merkel could haemorrhage support in a crucial regional election on May 9.

The emergency eurogroup summit has been arranged after the poll in North Rhine Westphalia, where defeat could cost Merkel her majority in the upper house in Berlin only eight months into her second term and condemn her to four years of legislative gridlock.

In Berlin today she was joined by other central players – Strauss-Kahn, and Jean-Claude Trichet, head of the European Central Bank and guardian of the euro – to hammer out the final details of the rescue package.

However reluctant she is to come to Greece's rescue, her wriggle room is narrowing quickly as the crisis escalates to the point where Athens will not be able to borrow money when it needs to.

If Germany is being blamed for foot-dragging and making a bad situation a lot worse, Berlin is confident it is right. In the end, it will bail out Greece. But the price demanded will be high. Merkel appears determined that Greece will be the first and the last case of its kind.

Sticklers for fiscal rectitude and angst-ridden that other spendthrifts will turn the euro into an unstable, inflation-prone currency, the Germans fear they will weaken the euro if they reward Greek misconduct with billions of bailout. That's the moral hazard, seen from Berlin. Most others fear the impact on the currency's stability and longevity if the Germans don't cough up.

The Europeans and the IMF have already agreed on a €45bn package for Greece subject to Athens surrendering some of its fiscal sovereignty and bowing to a three-year programme of savage spending cuts and restructuring. But with the pace of events in the markets outstripping the attempts of Europe's politicians to get to grips with the crisis, there are widespread fears that Europe's first attempt to rehabilitate a fiscal delinquent may be coming too late and amount to too little.

The May 10 summit will be the third such meeting of European heads of government in as many months to deal with the emergency. With developments moving at a dizzying speed, it looks like a last chance.